Understanding and predicting athletic performance is important for setting athletes' compensation, optimizing training methods, developing rules for competition, wagering, developing tactics and strategies, and preventing injuries. Athletic competition combines the application of intentional, often precise, movements with uncertainties introduced by the environment and adversaries' actions.
Efforts to understand and predict the performance of athletes, both as individuals and as competitive teams, are grouped into two classes. In the first class, past athletic performance is evaluated using statistical moments of observed behaviors to estimate the future performance of a player or team. Batting averages in baseball, free throw percentages in basketball, first service percentages in tennis, and rushing yards in football are examples of statistical information that is used to evaluate and predict athletic performance. The underlying assumption of this class of method is that athletic activities are ergodic and stochastic.
This class of statistical methods is becoming more widely used as systematic measurements of athletic processes and events become more widespread. The ubiquity of high definition, high-speed video recording, wearable biological monitors, geospatial and local tracking systems for people and objects, and the like has produced huge sets of observational data from athletic events.
A second class of related art for evaluating and predicting athletic performance considers deterministic aspects of athletic activities such as the mechanics of cleats on turf, the ballistic trajectories of balls, the biomechanics of a thrower's body, collisional dynamics of contact sports, and the like. The influence of respiration, blood circulation, ligament strength, pharmacokinetics, and other physiological parameters are further examples of elements used in deterministic models of athletic performance. These methods presume that athletic performance is rigorously determined by initial conditions and mathematical equations that are not random.
A drawback of the first class of methods is that statistical attributes and predictions are based on associations rather than mechanistic, cause-and-effect relationships. A problem with assessments and predictions based solely on prior statistics is that they are ergodic. In other words, there is a presumption that the samples from which statistics are computed span the entire space of possible conditions. Yet another deficiency of the statistical method is that it is invalid for degrees of freedom that are not directly observed. These deficiencies limit the ability of the class of methods to interpolate and extrapolate from prior conditions. Another drawback of the first class of methods is that it fails to explicitly incorporate rules of the athletic event or competition.
A drawback of the second class of methods is that it does not account for underlying randomness in athletic performance. It is also often impractical to incorporate all relevant variables into a deterministic model. Yet another limitation of deterministic methods is that they can be chaotic. In other words, their nonlinearity can generate predictions that are too sensitive to initial conditions to be useful.